Rewrite as a simplified fraction. ${0.82\overline{3} = {?}}$
Explanation: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 823.3333...\\ 100x &= 82.3333...\end{align*}}$ Subtracting the two equations, we have: ${900x = 741}$ ${x = \dfrac{741}{900}} $ ${x = \dfrac{247}{300}} $